# Automatic differentiation of non-holonomic fast marching for computing most threatening trajectories under sensors surveillance

## TL;DR

This paper develops a method combining non-holonomic fast marching and automatic differentiation to compute optimal evasive trajectories and optimize surveillance placement in a monitored region.

## Contribution

It introduces a novel approach integrating non-holonomic fast marching with automatic differentiation for strategic surveillance and evasion planning.

## Key findings

- Efficient computation of optimal trajectories considering vehicle maneuverability.
- Gradient-based optimization of surveillance sensor placement.
- Demonstrated effectiveness in simulated surveillance scenarios.

## Abstract

We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the the monitored area, visit a target region, and then leave the area, while minimizing his overall probability of detection. Both players know the target region, and the second player knows the surveillance installation details.Optimal trajectories for the second player are computed using a recently developed variant of the fast marching algorithm, which takes into account curvature constraints modeling the second player vehicle maneuverability. The surveillance system optimization leverages a reverse-mode semi-automatic differentiation procedure, estimating the gradient of the value function related to the sensor location in time N log N.